Learning and exploiting mixed variable dependencies with a model-based EA

Abstract

Abstract-Mixed-integer optimization considers problems with both discrete and continuous variables. The ability to learn and process problem structure can be of paramount importance for optimization, particularly when faced with black-box optimization (BBO) problems, where no structural knowledge is known a priori. For such cases, model-based Evolutionary Algorithms (EAs) have been very successful in the fields of discrete and continuous optimization. In this paper, we present a model-based EA which integrates techniques from the discrete and continuous domains in order to tackle mixed-integer problems. We furthermore introduce the novel mechanisms to learn and exploit mixedvariable dependencies. Previous approaches only learned dependencies explicitly in either the discrete or the continuous domain. The potential usefulness of addressing mixed dependencies directly is assessed by empirically analyzing algorithm performance on a selection of mixed-integer problems with different types of variable interactions. We find substantially improved, scalable performance on problems that exhibit mixed dependencies.

Exploring trade-offs between target coverage, healthy tissue sparing, and the placement of catheters in HDR brachytherapy for prostate cancer using a novel multi-objective model-based mixed-integer evolutionary algorithm

“…Here, we give a brief outline of GAMBIT. More details can be found in literature [12]. GAMBIT is a parameter-free model-based EA capable of learning and exploiting di erent types of variable dependencies, through a clustering mechanism and an integrated dependency-models mechanism.…”

“…e same number of continuous subsets are added to the FOS, each containing every continuous problem variable. Additionally, l c + l d mixed subsets are added to the FOS by building another linkage tree constrained to merge discrete and continuous variables using a mixed mutual information metric, described in detail in [12]. Such mixed subsets allow for the consideration of discrete and continuous variables together, resulting in the ability to exploit potential mixed variable dependencies.…”

“…Optimization where discrete and continuous variables are present simultaneously is explored relatively less and is referred to as mixed-integer optimization. A recently introduced Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT) has shown to be an e ective approach to single-objective optimization in the mixed-integer domain [12], especially in the case of black-box optimization, meaning that no internal structure of the problem is assumed to be known in advance. is makes GAMBIT exible and easily adaptable for our multi-objective approach of BT pre-planning optimization.…”

GAMBIT - Genetic Algorithm for Model-Based mixed-Integer opTimization

“…Optimization where discrete and continuous variables are present simultaneously is explored relatively less and is referred to as mixed-integer optimization. A recently introduced Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT) has shown to be an effective approach to single-objective optimization in the mixed-integer domain [75], especially in the case of black-box optimization, meaning that no internal structure of the problem is assumed to be known in advance. This makes GAMBIT flexible and easily adaptable for our multiobjective approach of BT pre-planning optimization.…”

“…The same number of continuous subsets are added to the FOS, each containing every continuous problem variable. Additionally, l c + l d mixed subsets are added to the FOS by building another linkage tree constrained to merge discrete and continuous variables using a mixed mutual information metric, described in detail in [75]. Such mixed subsets allow for the consideration of discrete and continuous variables together, resulting in the ability to exploit potential mixed variable dependencies.…”